WITTGENSTEIN’S TRACTATUS 3.333 AND RUSSELL’S PARADOX; pp. 179–197

Authors

Urmas Sutrop

Abstract

In his ‘Tractatus logico-philosophicus’, Ludwig Wittgenstein declares that he has solved Russell’s paradox. He presents the solution in a prima facie simple formula “(∃Φ) : F(Φu) . Φu = Fu”. This solution is disregarded both by the Russellians and most Wittgensteinians. In this paper I try to read the above formula and translate it into a class membership language (CML). I show that this formula contradicts Russell’s logic. I investigate and compare the different forms of this formula in Wittgenstein’s manuscripts and in the different editions of the ‘Tractatus’. I also take a look at the different interpretations of this formula in literature. My position is that Wittgenstein created his own transcendental logic that can show self-referential (reflexive) sentences without reflexivity.

Keywords

Ludwig Wittgenstein, Bertrand Russell, paradox, logic, history of logic, history of philosophy

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